Originals: Fly Into the Mystery by Jonathan RIchman & The Modern Lovers (covered by Luna)

Jonathan Richman
I think Fly Into the Mystery might have been another song recorded in the 1973 sessions with Kim Fowley (although as mentioned in the entry on Don't Let Our Youth Go to Waste this is not clear-cut) - this recording is available on the Songs of Remembrance bootleg :
Live versions are available dating from as early as 1971 - such as this one from a recently unearthed bootleg:

It turned up officially on the 1977 release Rock and Roll With The Modern Lovers

Luna's version first turned up on the Benicassim 98 compilation listed as "Fly Into The Sun" and then on the Italian compilation Homesleephome2 and later on the digital only Lunafied.